# Sec12.7 - Sec.12.7 Extreme Values and Saddle Points A local...

This preview shows pages 1–2. Sign up to view the full content.

Sec.12.7 Extreme Values and Saddle Points A local minimum is a point in the domain that yields the smallest function value in a small region of the domain about it. A local maximum is a point in the domain that yields the largest function value in a small region of the domain about it. In dealing with multi-variable functions we may have a third type of point in the domain, called a saddle point, which appears as a maximum in one direction and a minimum in another direction! If the extreme points discussed above have the smallest (largest) function value in the whole domain, we say we have an absolute minimum (maximum). If f has a local maximum or minimum at (a, b ) and the first order partials exist, then they must equal zero. ( , )0 ( , xy f a b and f a b == . An interior point (a, b) of the domain is called a critical point (stationary point) if both first partials equal zero or if one of the first partials does not exist.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 4

Sec12.7 - Sec.12.7 Extreme Values and Saddle Points A local...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online